Chapter 13: Q. 35 (page 1004)

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
$\int \int_{R} x y^{3} d A W h e r e R = {(x, y) | - 2 \leq x \leq 2, - 1 \leq y \leq 1}$

Short Answer

Expert verified

The value of integral is 0

Step by step solution

Given information

We are given an integral $\int \int_{R} x y^{3} d A W h e r e R = {(x, y) | - 2 \leq x \leq 2, - 1 \leq y \leq 1}$

Use iteration method to evaluate integral

We get,

$\int_{- 1}^{1} \int_{- 2}^{2} x y^{3} d x d y = \int_{- 1}^{1} {[\frac{x^{2} y^{3}}{2}]}^{2}_{- 2} d y = \int_{- 1}^{1} [0] d y = 0$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
$\int \int_{R} x y^{3} d A W h e r e R = {(x, y) | - 2 \leq x \leq 2, - 1 \leq y \leq 1}$

Short Answer

Step by step solution

Given information

Use iteration method to evaluate integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32∫∫Rxy3dAWhereR={(x,y)|-2≤x≤2,-1≤y≤1}

Short Answer

Step by step solution

Given information

Use iteration method to evaluate integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32
$\int \int_{R} x y^{3} d A W h e r e R = {(x, y) | - 2 \leq x \leq 2, - 1 \leq y \leq 1}$